The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is , it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is , it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.
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September 2007
Technical Papers
Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves
Xue-qian Fang,
Xue-qian Fang
Department of Aerospace Engineering & Mechanics,
e-mail: fangxueqian@163.com
Harbin Institute of Technology
, Harbin 150001, China
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Chao Hu,
Chao Hu
Department of Aerospace Engineering & Mechanics,
Harbin Institute of Technology
, Harbin 150001, China and School of Aerospace Engineering and Mechanics, Tongji University
, Shanghai, 200092, China
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Shan-yi Du
Shan-yi Du
Department of Aerospace Engineering & Mechanics,
Harbin Institute of Technology
, Harbin 150001, China
Search for other works by this author on:
Xue-qian Fang
Department of Aerospace Engineering & Mechanics,
Harbin Institute of Technology
, Harbin 150001, Chinae-mail: fangxueqian@163.com
Chao Hu
Department of Aerospace Engineering & Mechanics,
Harbin Institute of Technology
, Harbin 150001, China and School of Aerospace Engineering and Mechanics, Tongji University
, Shanghai, 200092, China
Shan-yi Du
Department of Aerospace Engineering & Mechanics,
Harbin Institute of Technology
, Harbin 150001, ChinaJ. Appl. Mech. Sep 2007, 74(5): 916-922 (7 pages)
Published Online: August 16, 2006
Article history
Received:
May 18, 2006
Revised:
August 16, 2006
Citation
Fang, X., Hu, C., and Du, S. (August 16, 2006). "Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves." ASME. J. Appl. Mech. September 2007; 74(5): 916–922. https://doi.org/10.1115/1.2712238
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